How to set collision bounds for Armature object
Don't apply the physic to your character's Armature directly as Armatures aren't recognized as an Actual model object but only an unrendered object that makes your character's body part move (rig), If you want to make your character collide with other thing, try this:


Make sure that your char's armature and it's model have No Collision physic assigned.
Then, make a Cube and resize it to match with your Armature/Character's size and Place it around your character, You can rename the Cube as "charbound" if you want.
Set the Cube's physic to Dynamic and then Set the Cube as parent of your Armature (not the entire character).
Move the basic movement control in Logic Bricks from your char's Armature to the Cube, but don't move the Action or other Actuator more than Motion Actuator.
And at last, make the Cube Invisible (physic tab > enable Invisible button) and Box Collision Bound.


If you want to make him "jump", try using Servo Control Motion Actuator in Game Logic. by adding Z-axis Linear Velocity, Enabled Z-axis Movement and Adjust Z-axis Max/Min speed value then it would jump, make sure you activate the Collision Bounds on Physic Tab. Alternatively, you can use Character Motion Actuator and Enable "Jump" toggle there (Actually, I've never tried it. But I'm sure it can).